Reticle for telescopic gunsight and method for using

ABSTRACT

A gunsight reticle defines a system of dimensioned indicia spaced at specific separations to improve aiming accuracy of a gun. The indicia may include perpendicularly intersecting center vertical and center horizontal hairlines, and four (or more or less) horizontal range-marker lines disposed at specific angular separations below the horizontal hairline in bisected relationship with the center vertical hairline. Spacing of the range marker lines below the center horizontal hairline is proportional to bullet drop at selected ranges, depending upon ballistic characteristics of bullet used. Relative lengths of said range-marker bars on each side of the central vertical crosshair are proportional to a specific crosswind (say 10 mph) at target range reflected by respective range marker. The method involves employing this reticle to determine distance to target, and using distance thus determined to ascertain a precise aiming point on the reticle. These indicia also have other useful characteristics that allow the shooter to easily mentally calculate corrections for crosswind, moving targets and shooting at targets that are above or below the shooter at a significant angle.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. application Ser. No.10/306,505 filed on Nov. 27, 2002, which is a continuation of U.S.application Ser. No. 10/101,819 filed on Mar. 19, 2002, now U.S. Pat.No. 6,591,537, which is a continuation of U.S. application Ser. No.09/152,320 filed on Sep. 14, 1998, now U.S. Pat. No. 6,357,158, all ofwhich are incorporated herein by reference.

INCORPORATION BY REFERENCE

The following documents are incorporated herein by reference:

1. MALE MAGAZINE, November 1967, Article page 11, “The Man who RefusedTo Die”;

2. The Instruction manual previously entitled “The Perfect Shot” andcurrently titled “The TDS—TRI-FACTOR Mental Ballistics CalculatorSystem,” by Thomas D. Smith III;

3. The Instruction manual entitled “Tactical Stress Management,” byThomas D. Smith III;

4. The Instruction manual entitled “The TDS TRI-FACTOR Rifle ScopeSystem” by Thomas D. Smith III; and

5. The Instruction manual entitled “The ADINO Combat Rifle Scope System”by Thomas D. Smith III.

BACKGROUND OF THE INVENTION

1. Field of Invention

This invention relates to telescopic and other optical sighting systemsfor use on guns and other projectile delivering systems of all types butwill herein it will be described as primarily applied to telescopicsights on typical rifles. More particularly, this invention relates mostnaturally to a telescopic gunsight equipped with a transparent aimingreticle and a method for using that reticle on a gun but it is certainlynot constrained to that specific application.

2. Description of Prior Art

It is well known that the line of sight between a shooter's eye and atarget is a straight line, whether using “iron” sights or a telescopicsight, while the trajectory of the projectile is never a straight line(when passing though a gravitational field, the trajectory follows aballistic parabola), which becomes of particular importance forprojectile flights covering long distances. Accordingly, in order toachieve sufficiently accurate shot placement, it is essential either to“sight in” the rifle (or other projectile delivering system: hereafter“gun”) to produce the projectile (hereafter, bullet) to the desiredaiming point at a specific fixed target distance or to know both thedistance from the gun to the target and the trajectory characteristicsof the bullet used. Trajectory characteristics for commercial bulletsare related to initial launch velocity and are known or are easilyobtained from either the manufacturer or from trajectory charts such asINGALLS' tables.

Telescopic gunsights, often referred to as “scopes,” generally contain atransparent flat disk reticle positioned in a plane perpendicular to theline of sight through the scope. The reticle conventionally has a singlevertical crosshair (or hairline) and a single horizontal crosshair (orhairline), which intersects the vertical hairline near the visual centerof the reticle and the scope. The point of intersection of thesecrosshairs constitutes the primary sighting point for the scope,representing site of bullet impact at a chosen (zero) distance.

In modern scopes, the gunsight is most commonly moveable in vertical andhorizontal directions by way of calibrated adjustment screws located onthe scope exterior (internal adjustments); in some older and a few newerand new scopes, the gunsight is adjusted by devices within the scopeattachment system (external adjustments). Method of adjustment has nosignificant influence upon reticle design or use.

By firing one or more shots and making compensatory adjustments of therelative position of the reticle center point, the shooting system,which is comprised of rifle, bullet type and velocity, scope and shooteris “zeroed in” so that aiming position of the reticle crossed hairlinesor reticle center point coincides with point of bullet impact on thetarget.

In certain scope sighting systems, the reticle has a series ofevenly-spaced secondary horizontal hairlines that intersect the verticalhairline below the center horizontal hairline. In those systems, therespective points of intersection of the secondary hairlines with thevertical hairline are typically used to estimate bullet impact points atdistances progressively greater than that at which the rifle was “zeroedin” with the main (center) horizontal crosshair. However, in order toutilize these secondary horizontal crosshairs with accurate andpredictable results, the shooter must know distance from gun to targetwith a significant degree of precision.

Various types of range finder systems have been disclosed for telescopicgunsights. For example, U.S. Pat. No. 1,190,121 to Critchett discloses areticle having a series of target-spanning rulings disposed above abaseline, the rulings corresponding to associated shooting distances. Inuse, the shooter ascertains which ruling above the baseline makes themost closely embracing fit on the target, thereby determining theshooting distance (target range). A separate crosshair aiming point isincluded in the reticle for use in association with each chosen rulingabove the baseline.

The principle of the Critchett target-spanning rulings is that certaintargets are of known, or at least estimable size. For instance, it is afairly accurate estimate that for mature deer or antelope, the distancebetween the top of the back at the shoulders and the bottom of the chestcavity is about 18 inches. The target-spanning rulings are spaced apartsuch as to span a known target size at a known range. This manner ofdistance measurement is consistent with conventional trigonometricconsiderations wherein the triangle defined by the height of the targetand the viewing angle through the telescope's optical system can beconsidered a right triangle, which accordingly establishes the length ofthe base line distance to the distal side of the triangle, namely thedistance to the target.

U.S. Pat. No. 3,392,450 to Herter et. al. discloses a reticle having aseries of target-spanning circles of different diameters whichcorrespond to associated shooting distances. Employing the same basicdistance-measuring concept as Critchett, the shooter employs for aimingpurposes, that crosshair which corresponds to the selected circle.

U.S. Pat. No. 3,190,003 to O'Brien concerns a range-finding reticle fora telescopic gunsight having single centered vertical and horizontalhairlines. The portion of the vertical hairline below the horizontalcenterline is provided with widened bar regions extending variouslengths below the centerline. Each bar subtends a target of known size.By finding which widened region corresponds to the height of the target,the shooting distance is estimated.

U.S. Pat. No. 3,431,652 to Leatherwood discloses a telescopic gunsightwherein the distance to the target is determined by movement of upperand lower horizontal hairlines along a fixed vertical hairline in amanner so as to bracket the target. Once bracketed, the intersection ofthe lower horizontal hairline with the vertical hairline serves as thecrosshair aiming point. In this aiming process, the alignment of thescope changes with respect to the gun barrel, whereby the allowance fordistance is achieved when the centered crosshair is sighted directly onthe target.

U.S. Pat. No. 3,492,733 to Leatherwood discloses a distance measuringsystem for a variable power telescopic sight that is pivotally moveablein a vertical plane with respect to the gun barrel upon which it ismounted. Cams within the scope and rotatable by external means achievevertical movement of the scope so that horizontal framing hairlines willfit the target. A specialized cam must be installed into the scope foreach particular type of ammunition employed.

U.S. Pat. No. 3,948,587 to Rubbert concerns a variable power telescopicsight having a reticle provided with a vertical hairline, a centerhorizontal hairline and three horizontal framing lines disposed belowthe center horizontal hairline. Aiming is achieved by positioning eitherthe center crosshair or lower crosshairs on the target, as dictated bythe observed fit of the target within the framing lines.

U.S. Pat. No. 4,403,421 to Shepherd discloses a telescopic gunsighthaving spaced apart primary and secondary reticles which are moveablerelative to each other. The secondary reticle is also moveablevertically and horizontally within the plane of the reticle. Themoveable two reticle system facilitates adjustments for windage andelevation. Distance to the target is ascertained by framing indicia onthe secondary reticle.

The telescopic sights disclosed in the aforementioned prior art patentsare often of limited usefulness insofar as they do not address many ofthe several factors that need to be considered in the accurate aiming ofa rifle under field conditions. Such factors include:

a) distance to target

b) drop of bullet caused by force of gravity

c) hold-over or hold-under aiming points

d) wind drift correction

e) correction for phenomenon associated with gyroscopic forces on agyroscopically stabilized bullet (sometimes referred to as)

1) Yaw of Repose effects (vertical displacements)

2) Magnus effects (horizontal displacements)

These latter result from the effect of cross-wind or shooting eitherup-hill or down-hill.

Older reticle systems often require that the shooter look away from thetarget in order to make compensating adjustments and almost alwaysrequire complicated mental or physical manipulations. Some of thesedesigns may render the scopes difficult or slow to use, and some requiremoveable mounting on the rifle, a situation which typically subjects thescope to inaccuracy after repeated use or abuse in rugged fieldconditions. Moreover, correct use of any of these systems alwaysrequires the shooter to manage extraordinary mental work in what canalready be a stressful situation. It is proven that such additionalstress is associated with decreased performance potential.

SUMMARY OF THE INVENTION

The present invention is embodied in a reticle design concept for agunsight and “sticker” system. By firing shots to perform a simple droptest, the shooter can know which sticker to choose in order toautomatically calibrate this reticle to measure distance to any sizetarget, to provide precise drop compensation aiming points for specificmeasured ranges beyond the normal point-blank (zero) range for anybullet, to automatically provide precise aiming points compensating forcross-winds and up-hill or downhill shooting conditions, and to providean accurate lead point aiming corrections for moving targets, therebyproviding an accurate and effective method for aiming the rifle, allwith relatively simple and fast mental work that does not requireextraordinary effort by the shooter or any knowledge of the particularballistic characteristics of load or gun to which this system isapplied.

It is critical to note that the TDS system combines three criticalfactors:

1) specially designed reticle;

2) specially designed stickers (durable visual keys intended to beattached to the gun);

3) test firing to prove required sticker for the system and use.

The telescopic sighting system incorporates an optical system comprisedof a forward objective lens element, a rear eyepiece lens element andintervening erector lens element, the elements being protectivelyconfined within an elongated tubular housing adapted to be affixed to afirearm, such as a hunting rifle (but not restricted to such use andapplication—with proper adjustments, this system can just as well beapplied to the sighting system on a bow, handgun, artillery piece,airplane or other instrument). The improvement provided by the presentinvention comprises addition into said optical system within saidhousing of a transparent reticle having indicia which simultaneouslyprovides accurately both the function of distance measuring,range-specific aiming as well as wind related and other trajectorycorrections. The reticle is positioned between the objective lenselement and the erector lens element. The indicia incorporatesorthogonally intersecting center vertical and horizontal hairlines, andfour (or more or less) horizontal combination range-marker and wind barlines, which are disposed below the center horizontal hairline with veryspecific vertical spacings and intersecting in a bisected relation thecenter vertical hairline.

Note that other carrier systems and other specific designs for any meansof achieving the same aiming goals through the same basic functionality,which is derived from recognition of the parabolic nature of aprojectile trajectory, are envisioned and are specifically recognizedand claimed as intellectually and functionally similar and thereforealso protected by this application.

The specific and precise configuration and positioning of the rangemarker and wind bar lines enables the shooter to mentally compute therange to the target and allow for bullet drop, wind drift, gyroscopiceffects, up-hill or down-hill angle shots and target lead. With modestpractice, a typical shooter can learn to accomplish these tasks withinin a split-second. The specific ratio of the spacings of these secondaryindicia is critical to the functionality of this system. The accuracyachieved by this reticle promotes shooter confidence which in turn leadsto shooter proficiency. Similarly, the simplicity of the basic member ofthis system, as described herein, leads to simplicity of preciseapplication.

This system can also include range marker bars that intersect thevertical axis at a slight angle. The purpose of this characteristic isto automatically correct for the elevation component of wind drift. Itis a recognized fact that crosswinds do cause bullets to raise or droprelative to the trajectory that would occur without a crosswind. Thischaracteristic is not described in the drawings but is a recognizedpotential feature that can have significant value in specificapplications, such as airplane and artillery sights, but is not limitedto such applications.

The basic reason that this system works relates to the following facts.First, all projectiles fired in the gravitational field and atmosphereof the Earth travel in a parabolic trajectory. Shape of the curvedescribed by this trajectory depends upon angle of fire (with respect tothe horizontal), atmospheric conditions and gravitational factors,projectile exit velocity and the ballistic efficiency of the projectile(which is described as ballistic coefficient, or BC, for bullets). It isa fact that to a reasonable approximation, all such curves contain asection near the beginning (within the typical useful range of anyprojectile launching device) that is shaped very similar to a similar alike section from any other trajectory curve. By applying an expansionin the longitudinal direction and possibly a rotation about the verticaland horizontal axis to the curve represented by the slower projectile,to a first approximation (and close enough for practical purposes), suchsections of the two curves will follow indistinguishable paths. Refer toFIG. 12.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side elevation view of a telescopic sight embodying thepreferred type of the present invention mounted upon a gun of the typecommonly used for hunting, target shooting and related practices.

FIG. 2 is a schematic illustration of the internal components of avariable power telescopic sight of the type shown in FIG. 1.

FIG. 3 is an enlarged view showing an aiming reticle component of thesight of FIG. 1 as it appears to the user of the sight.

FIGS. 4A, 4B and 4C illustrate the use of calibration grids for learningthe use of the scope of this invention.

FIG. 5 illustrates the use of the scope of this invention on largetargets.

FIGS. 6A and 6B illustrate the use of the scope of this invention on asmall target.

FIGS. 7-11 exemplify sighting images perceived by the shooter in variousshooting situations.

FIG. 12 illustrates the reticle depicted in the form of a decal fortaping upon the objective extremity of the scope or some other handylocation. The left-hand Grid Line column serves as a reminder to denotethe actual number of lines with which to divide into the animal's ortarget's outline for height measurement. When determining distance totarget, the upper right column, Aiming Point at level angle, denotesbullet impact point for a “6 Factor” gun zeroed or sighted-in at 200yards. Using the grid-line center point, at 100 yards the bullet impactwill be 1.84 inches (about 2 inches) high, and at 200 yards the impactpoint will be on target (zeroed)—200 yards is a typical “zeroing” rangefor such a gun and load. At 300 through 600 yards the lower indicia(crosshairs) provide a precise aiming point at each respective stateddistance (progressively, 300, 400, 500 and 600 yards) to give thedesired impact point. The upper center column, Aiming Point Grid Line at45 degree Angle, denotes the angle correction when shooting uphill ordownhill. For a “6 Factor” gun, simply move up the equivalent of onecrosshair (about 2″ of angle subtention) for a 45° angle shot.

FIG. 12 illustrates the fundamental reason that this system works:Sections of significantly different trajectories forced into relativecorrespondence through the simple expedient of rotation and horizontalscaling.

FIG. 12 (Rotation and horizontal scaling yields similar sections for alltrajectory curves).

FIGS. 12-26 provide additional description of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENT (FOR THE PURPOSES OF CLARIFICATIONONLY)

Referring to FIGS. 1-3, a telescopic sight 10, embodying this inventionis shown attached by a suitable mount 35 to a gun 12. The sight 10 isformed by a tubular housing 11 containing a forwardly positionedobjective lens element 13, a rearwardly positioned ocular or eyepiecelens element 14, an intervening erector lens element 15, and a reticle16 disposed between the objective lens element 13 and the erector lenselement 15. In the case of vari-focal or zoom scopes, a positionallyadjustable magnifying lens 17 is associated with the erector lenselement 15. The exterior of the housing 11 may be equipped withrotationally moveable features 36 for adjusting focus, parallax,magnification ratio, windage and elevation. Each of the various lenselements may be single lenses or combinations of lenses, either alignedin proximity or glued together or a combination of these compositions.

The reticle 16 is a circular, planar or flat transparent panel or diskmounted within the housing 11 in perpendicular relationship to theoptical axis or line-of-sight 18 through the scope, and is positionedbetween the objective lens element 13 and the erector lens element 15,typically at a site considered to be a front focal plane of the opticalsystem within the housing. The reticle 16 contains fine etched lines orhairline indicia comprising a center vertical hairline 19 and a centerhorizontal hairline 20, which orthogonally or perpendicularly intersectat a center point 26. The reticle further defines first, second, thirdand fourth horizontal range and aiming marker hairlines 21, 22, 23 and24 (or other designs as may be appropriate to specific applications)respectively intersecting the vertical hairline below the center point26 and vertically spaced apart and of sequentially increasing length.Each such range and aiming marker hairline 21, 22, 23, and 24 isbisected by the center vertical hairline 19, in the present design in ahorizontal manner but potentially in an angled manner as necessary toaccount to the vertical component of wind drift, etc.).

We must also note that it is feasible to present a virtual reticle intothe sighting system by other means, chiefly electronically, and that theabsence of a physical reticle in no way alters the functionality of thepresent invention; therefore, any means of generating aiming points thatachieves the same goal as that described herein is fundamentallyidentical in nature and is also claimed.

Each combination of a gun and bullet or cartridge must be initiallysighted in at 200 yards, or other selected basic zero range, whichdepends critically upon the ballistic characteristics of the specificbullet (refer to FIG. 12). The center point 26 then represents the basicsighted-in bullet impact point. The points of intersection of saidfirst, second, third and fourth range marker lines 21, 22, 23, and 24with said vertical hairline, designated first, second, third and fourthalternative aiming points 30, 31, 32 and 33, respectively, representsighted-in bullet impact points at distances that are a function ofbullet trajectory for the specific load used. For example, for a bulletand gun determined to be a “6 factor” system, as will be explained, theaiming points are for distances of 300, 400, 500 and 600 yards,respectively.

A “6-factor” gun and bullet combination is a system that produces a 6inch drop from a “sight-in” impact zero point at 200 yards to the bulletimpact point when the same combination of gun, bullet and scopeadjustment settings is fired at 300 yards, using the center point 26 asthe aiming point. Bullets of different characteristics and velocity(different gun and bullet combinations) will produce different“factors.” Thus the aiming points 30, 31, 32 and 33 will correspond todifferent distances or ranges, which the shooter, knowing thecharacteristics of the bullet, will take into consideration when aimingand firing.

The aiming points 30, 31, 32 and 33 are useful because the trajectorycurves of different bullets are similar, even though the bullets traveldifferent distances—some similar-length section of each curve, whethercloser to the gun or further from the gun, will have a sufficientlysimilar shape to allow accurate use of this system (refer to FIG. 12).

The radially outer or distal portions of the center vertical hairline 19and center horizontal hairline 20 are widened to form relatively wideror heavy posts 25 whose radially directed innermost extremities 28 aredisposed on a circular locus about the center point 26. However, this isnot a design limitation of this system, the main horizontal and verticalcrosshairs can be of any particular design, as might be necessary toprovide the best performance in any particular application and couldeven be partially or fully absent as when only a central dot is used.

The various dimensions and spacings of the indicia on the reticle 16 areconveniently expressed as inches of subtention or angle at 100 yards,rather than the actual engraved dimensions on the reticle lens itself.Accordingly, the width of each of the posts 25 is 5.5 inches ofsubtention, and the width of the hairline portions of the centervertical and center horizontal hairlines 19 and 20, respectively, is 0.6inches of subtention. The distance between the center point 26 and theinnermost extremities 28 of the posts 25, that is the length of thecenter vertical and horizontal hairlines 19, 20, respectively, is 25inches of subtention. However, it must be noted that these specificdimensions and ratios of dimensions are not the only possible usefuldesigns. The important issue is usefulness in the specific application.

The distances or width of the separation between the horizontal hairline20 and the first, second, third and fourth range lines 21, 22, 23, and24 below the center point 26 are 2.0, 4.8, 7.5 and 10.5 inches ofsubtention, respectively—but other designs are feasible for otherapplications. Typically four, marker lines are typically of equal 0.3inch width of subtention and are typically straight and orthogonally orperpendicularly bisected by the lower half or lower portion of thecenter vertical hairline 19; however, other line thicknesses andnon-orthogonal intersections with the vertical line are feasible and maybe preferable in some applications. When four such lines are used, thelengths of the first, second, third and fourth range marker lines are4.12, 5.90, 8.32 and 9.72 inches of subtention, respectively; however,other lengths are feasible and may be preferable in someapplications—the lengths specified above correspond to requiredcorrections for a 10 mile per hour true crosswind component, which is awind speed to which many experienced shooters can recognize and relate.

The foregoing dimensions are empirically derived and are critical to theaccuracy and ease of use of this system in the standard application(such as a hunting rifle)—these datum are fundamental to the concept.However, one can also envision more complex systems that might be usedfor other applications wherein the extended range elevation aiming linesmight be thinner, longer and include enlarged “dots” at specificintervals to indicate corrections for various true crosswind velocitiessuch as 5, 10, 15 and 20 miles per hour, etc. Moreover, for otherapplications, this basic concept could be extended to include designshaving more than four range marker bars. No such application andembodiment should be considered to fall outside the basic tenants ofthis concept and therefore, this application is not limited to thespecific design described herein; rather, this concept should beunderstood to cover any application wherein the spacings and lengths ofthe range lines incorporate the required characteristics so as tocorrespond to the parabolic nature of a projectile trajectory at anyspecific incremental (or other useful) range interval and windcondition. The central point of this art is that it uniquely recognizesthe parabolic drop and crosswind deflections characteristics of realprojectiles.

As noted elsewhere, in the particular embodiment described herein, the“factor” for a particular gun and bullet combination is determined bysighting it in at 200 yards using the center point of the reticle. Usingthe same 200 yard sight center point, a group of shots is then fired at300 yards and average drop (in inches) is measured. This figure becomesthe “factor” that is used to compute vertical bullet drop, wind driftdeflection, both horizontally and vertically, and gravity correction forboth uphill and downhill angle correction for that particular gun andloading.

Bullet drop is progressively curvilinear (following a parabolic curve),and is well predictable out to about 0.72 seconds of free flight (450yards for a .308 Winchester; 500 yards for a 30/06; 600 yards for a 7 mmRemington Magnum; and 700 yards for a 30/378; all when used with highenergy maneuverability bullets—traditionally known as bullets having astreamlined shape and a relatively high ballistic coefficient). Bulletdrop for a 6-factor gun and bullet combination for example, results in a6-inch drop at 300 yards. This factor is tripled to predict 400-yardbullet drop. This 400-yard drop is doubled to predict 500 yard drop. For600-yard drop, the 500 yard drop is doubled and ten (inches) issubtracted from that result. This corresponds to a formula used todetermine the spacing of these indicia.

For instance, a 6-factor bullet (150 grain 7 mm. Remington Magnum firedat 3,200 fps) computes thusly:

a. 300 yard drop: 6″

b. 400 yard drop: 3×6=18″

c. 500 yard drop: 18×2=36″

d. 600 yard drop: 36×2=72−10=62″

In other words, for a 6-factor gun and bullet that is zeroed at 200yards, the bullet drops 6″ @ 300 yards, 18″@ 400 yards, 36″@ 500 yards,and 62″@ 600 yards. Other specific formula and extensions to longertimes of flight are feasible so long as those describe usefulcharacteristics of real projectiles.

A reticle embodying the present invention having the abovecharacteristics and dimensions, will produce sufficiently accurate shotswhen using the respective reticle aiming points at the determineddistances. For gun and bullet combinations that have a factor other thansix, center impact distances corresponding to the various aiming pointsmust be calculated accordingly. See Table I.

It is a useful fact that variable magnification scopes (commonlyreferred to as variable power scopes) with the reticle positioned in thefirst focal plane (in this design, adjusting the power setting of thescope also adjusts the absolute apparent spacing between the rangeindica) can be used to automatically adjust the described reticle, asrequired to provide to correct holdover for practically any “factor” gunand load by the simple expedient of adjusting the power setting to therequired value, so as to generate the correct spacing of the indicia. Insome applications, it might be necessary to alter the basic zero rangeand range increment but such correspondence will always be feasible.

Use of a scope utilizing this invention for measuring target distancemay best be visualized by referring to the grid line charts as shown inFIGS. 4A, 4B and 4C. Each grid line chart consists of a series ofnumbered horizontal straight lines sequentially spaced an inch apart(inch of subtention at 100 yards or approximately one minute of angle)and assumed to be visibly distinct in the scope at the indicated ranges.A target such as a 9-inch tall prairie dog is drawn to occupy the topnine lines of a chart, as shown in FIG. 4A, and assumed to be placed ata range of 100 yards. The scope is then sighted onto said 100 yardtarget, producing the view shown in FIG. 4B wherein the top of theprairie dog is placed at the center point 26, and the bottom of theprairie dog falls between the third and fourth range marker lines,namely between 7.5 and 10.5 inches of subtention from the center point26. By interpolation, the bottom of the target, having an actual heightof 9 inches, is 9 inches of subtention from the center point 26. It isaccordingly ascertained that the 9-inch high prairie dog target islocated at a shooting range of 100 yards.

It should be noted that the target heights subtended by the horizontalrange marker lines increase in direct arithmetic proportion to thedistance of the target from the gun. Therefore, at 200 yards, the first,second, third and fourth range marker lines measure targets of 4, 10, 15and 21 inch actual heights (rounded), respectively. At 300 yards, thefirst, second, third and fourth range marker lines measure targets of 6,15, 22.5 and 31.5 inch actual heights (rounded) respectively. At 400yards, the first, second, third and fourth range marker lines measuretargets of 8, 20, 30 and 42 inch actual heights (rounded) respectively.

When the same 9-inch prairie dog target is viewed for example at 300yards, the view through the scope is as shown in FIG. 4C, wherein thetarget appears much smaller because of the distance at which it islocated, and the range marker lines now correspond to progressive actualheights of 6, 15, 22.5 and 31.5 inches respectively in descending orderdown said center vertical hairline. Now, with the top of the head of thetarget at the center point, the bottom of the target will be locatedbetween the first and second range marker lines. This positioncorresponds to 3 inches actual height at 100 yards or 9 inches actualheight at 300 yards. It follows, that knowing the actual height of thetarget, one can easily determine target range. In other words, in orderto determine distance to target, target height is divided by inchreading on reticle. In the example of FIG. 4C, the 9 inch target wouldmeasure 3 inches on the reticle; accordingly, target range is 9÷3=3(×100), or 300 yards.

Once the shooter has determined target range, and when the shooter knowsthe factor of the gun and bullet being used, the scope can be accuratelyaimed by centering the appropriate indicia along the vertical hairlineupon the desired location of bullet impact. For example, with a“6-factor” gun and bullet combination, and having ascertained that thetarget is located at 300 yards, and knowing that the main reticle centerpoint 26 is for a 200 yard range, the next lower aiming point,consisting of the point of intersection 30 of the vertical crosshair 19with the first range marker 21, corresponding to 300 yards, is, underideal conditions and with a stationary target, used as the aiming pointfor a direct hit.

Use of this reticle with respect to a Rocky Mountain Elk having anestimated 25 inch chest height is illustrated in FIG. 5. It is seen thatthe 25 inch chest is spanned by about 5 inches of subtention of reticledistance. Accordingly, the range is 25÷5=5 (×100), or 500 yards, andaiming point 32 is employed for shooting, centered upon target, againthis assumes a “6-factor” gun and bullet combination, ideal conditionsand a stationary target.

Compensation must be made for bullet deflection due to wind drift. Tothis end, the gun must be pointed into the wind. This is accomplished bymoving the reticle aiming point in the opposite direction an appropriateamount. For this purpose, the applicable “factor” becomes the 10 mphwind correction or drift, applied in a linear manner.

a. at 300 yards the drift is 6″;

b. at 400 yards the drift is 6+6=12″;

c. at 500 yards the drift is 12+6=18″;

d. at 600 yards the drift is 18+6=24″.

For a 5 mph wind, the drift values would be one-half the 10 mph values,and a 20 mph wind would require twice the 10 mph values and similarlyfor other true crosswind velocities.

The sight picture for shooting at a 9-inch high prairie dog at 100 yardsis illustrated in FIG. 6A. The sight picture for shooting at a 9-inchhigh prairie dog at 600 yards with a 10 mph left crosswind isillustrated in FIG. 6B. The view through the scope when shooting at atarget at 500 yards is illustrated in FIG. 7. FIGS. 8 and 9 illustrateadjusted aiming points to compensate for 10 mph and 20 mph right-to-leftcrosswinds, respectively. For this purpose, the ends of the range markerlines, having the above lengths, constitute aiming points to compensatefor 10 mph winds at the respective ranges. Length of the range markerbars on each side of the vertical centerline are one half the totallength or 2.06, 2.95, 4.16 and 4.86 inches of subtention at 100 yardsrespectively.

Compensation must also be made for the effect on the path of the bulletof the spinning thereof. The rifleman's idiom designates this as a“Magnus effect.” It may also be referred to as “Yaw of Repose.” theseare the vertical and horizontal elements of deflection in a crosswindwhen considering a gyroscopically spinning projectile or missile.

The formula for compensating for the potential worst case effect ofMagnus is to adjust ¼th the total value by sliding that point onto thetarget. In the illustration of FIG. 10, there is shown the aiming pointas an interpolated point left one equal wind bar (10 mph) and ¼ abovethe left tip of the third range marker line. (Unusually low-draghigh-speed bullets may react to Magnus only a small percentage of theadjustment in FIG. 10; however, hunting bullets do not fall into thiscategory.) The rule is to construct a “kill zone” on the target and thenhold “worst and best” Magnus movement so that the bullet is aimed withsufficient accuracy to intersect the kill zone.

Computing simultaneous Magnus and Yaw of Repose values and crosswindvalues:

1. With conventional (right-hand) twist barrels, these effect make thebullet rise with a right-to-left crosswind, drop with a left-to-rightcrosswind.

2. Add ¼th the horizontal value vertically to the final aiming pointusing the reticle wind bar as a transparency overlay.

As noted previously, it is also possible to incorporate automaticvertical-component crosswind correction into the range markers byaligning those at a slight angle to the horizontal so that the sightingcorrection for a crosswind automatically incorporates the requiredcorrection for the vertical component of wind drift. While not embodiedin the accompanying sketches, this method is claimed and recognized as alogical extension and improvement on the basic concept of this reticledesign. It is recognized that this method would require separate scopesfor guns with reverse rifling twist directions and for guns used in thesouthern hemisphere and might require special angles for guns used atcertain locations. However, for the vast majority of hunting gunapplications, one basic correction angle would suffice to providesufficient accuracy of correction as to achieve the required shotplacement accuracy.

When shooting uphill or downhill, bullet impact point will be higherthan when shooting level at the same total target distance. In otherwords, when computing uphill or downhill gravity values, it must benoted that angle shots require less hold-over, that is the aiming pointis moved upwardly on the reticle, because of a lesser gravity pullalthough bullet drag remains the same. A sight picture and aiming pointfor a “6-factor” gun and bullet at a 45° up-hill shot at 500 yards slantrange is illustrated in FIG. 11. The appropriate sighting adjustment insuch situation is to move up one range marker line for a 45 degreeangle, twice that or two range marker lines for a 60 degree angle, andone half that or up one-half the distance between appropriate rangemarker lines for a 30 degree angle.

The formula or adjustment for a 60° angle shot, for example, is asfollows:

a. at 200 yards, raise the aiming point an amount equal to ⅔rds of thefactor, or 4″;

b. at 300 yards, double the 200-yard value, or 8″;

c. at 400 yards, double the 300-yard value, or 16″;

d. at 500 yards; double the 400-yard value, or 32″.

The reticle of the present invention performs with each gun and bulletwith the same precise degree of accuracy. The shooter is thus provided asimilar but unique reticle decal for each combination. It must bestressed that the associated decals are an integral part of this systemand as such, the concept of application specific decals is also part ofthis art.

While a single reticle constructed as described above may be used formost gun and bullet combinations, specialized reticles may be needed forcertain particular gun and bullet or cartridge combinations, scopemagnifications and unusual applications. Therefore, the ratios ofindicia spacings and lengths are not unique and other ratios of andlengths can have value for specific applications, so long as thesecorrespond to range-finding functions, etc., as describing a parabolictrajectory, the design will be an obvious derivative of this basicconcept. This is a parametric design issue and the critical factor ofinterest is that specific ratios of spacings and lengths are required toproduce useful results.

It is further to be stressed that with this design the shooter need notdivert attention from the image in the scope for first determiningdistance and other corrections and second for finding the proper aimingpoint.

A telescopic gunsight utilizing this invention is particularly wellsuited for shooting at moving targets. It is generally known that a deerstarts running at about 12.5 mph. The distance between the reticlecenter point 26 and the innermost extremities 28 of the posts 25compensates for a target moving at 12.5 mph. Further adjustments can bereadily made for targets moving at other estimated speeds and angles, indirect proportion to the 12.5 mph speed adjustment.

The final sight picture provided by the reticle embodying the presentinvention, corrected for range, wind, external ballistics, and targetmovement results in a straight line aim and shot at the target in thesame manner as a point blank range shot. This enables the shooter tohave much more confidence in the result and therefore to more easilyachieve accurate shot placement.

Using a reticle of the present invention, observing the targetconditions, and applying the foregoing simple mental calculations, anaiming point on the reticle is selected and centered on the desiredtarget impact point. This can be done quickly with less stress or doubt,when compared to other systems. The shooter can then concentrate onfiring the gun in a relaxed mode with a minimum of movement or “jerk” ofthe gun and then “look the bullet into” the target—this is otherwisecalled “follow through” and has long been recognized as critical tomarksmanship.

While particular examples of the present invention have been shown anddescribed, it is apparent that changes and modifications may be madetherein without departing from the invention in its broadest aspects.The aim of the appended claims, therefore is to cover all such changesand modifications as fall within the true spirit and scope of thisinvention.

A final point of significant value revolves around the differencebetween first and second focal plane reticle placement in a variablepower scope. The former design provides for a means of making any“factor” reticle design fit any “factor” application. The disadvantageof this method is that it requires use of the variable power scope onlyat one specific power setting for the particular application. Thedisadvantage of the latter method is that it requires use of a specific“factor” reticle. Each system has advantages and this art covers any andall such applications.

1. In a telescopic gunsight having an optical system comprised of aforward objective lens element, a rear eyepiece lens element andintervening erector lens element, the elements being aligned upon anoptical axis constituting a line of sight and protectively confinedwithin an elongated tubular housing adapted to be securely affixed to agun, the improvement comprising: the addition into the optical system ofa transparent reticle having distance-measuring and aiming indicia, theindicia comprising, orthogonally intersecting center vertical and centerhorizontal hairlines, four horizontal range-marker hairlines ofsequentially incremental length disposed below the center horizontalhairline and each intersecting the center vertical hairline.
 2. Thetelescopic gunsight in accordance with claim 1 wherein the intersectionof the center vertical and center horizontal hairlines constitutes acenter point which defines a bullet impact point at 100 and 200 yards.3. The telescopic gunsight in accordance with claim 2 wherein the sitesof intersection of the first, second, third and fourth range-markerhairlines with the vertical hairline constitute first, second, third andfourth alternative bullet impact points, respectively, at ranges of 300,400, 500 and 600 yards, respectively.
 4. The telescopic gunsight inaccordance with claim 1 wherein the dimension of the various features ofthe reticle correspond to inches of subtention at 100 yards.
 5. Thetelescopic gunsight in accordance with claim 4 wherein the centerhorizontal hairline includes two radially distal portions each forming apost having radially directed innermost and outermost extremities, andwherein the distance between the center point and each of the innermostextremities of the posts is about 25 inches.
 6. The telescopic gunsightin accordance with claim 4 wherein the distances of separation of thefour range marker lines from the center point are such as to cause thesequential spacing between the range marker lines to progressivelyincrease.
 7. The telescopic gunsight in accordance with claim 4 whereinthe distances of separation of the first, second, third and fourth rangemarker lines from the center point are about 2.0, 4.8, 7.5 and 10.5inches, respectively.
 8. The telescopic gunsight in accordance withclaim 4 wherein the lengths of the first, second, third and fourth rangemarker lines are about 4.12, 5.90, 8.32 and 9.72 inches, respectively.9. A reticle for use in a telescopic gunsight, the reticle comprising: acenter vertical hairline and a center horizontal hairline intersectingin an intersection point; a first range-marker disposed below the centerhairline and at a first distance below the center horizontal hairlineand intersecting the center vertical hairline; a second range-markerdisposed below the first range-marker and at a second distance below thecenter horizontal hairline and intersecting the center verticalhairline; a third range-marker disposed below the second range-markerand at a third distance below the center horizontal hairline andintersecting the center vertical hairline; a fourth range-markerdisposed below the third range-marker and at a fourth distance below thehorizontal hairline and intersecting the center vertical hairline; andwherein the various features of the reticle correspond to inches ofsubtention at 100 yards, and the first distance is about 2.0, the seconddistance is about 4.8, the third distance is about 7.5 and the fourthdistance is about 10.5.
 10. The reticle in accordance with claim 9wherein the first, second, third and fourth range-markers are horizontalhairlines of sequentially incremental length
 11. The reticle inaccordance with claim 10 wherein the lengths of the first, second, thirdand fourth range marker lines are about 4.12, 5.90, 8.32 and 9.72inches, respectively.
 12. The reticle in accordance with claim 9 whereinthe intersection of the center vertical and center horizontal hairlinesconstitutes a center point which defines an approximate bullet impactpoint at 100 and 200 yards, and wherein the sites of intersection of thefirst, second, third and fourth range-markers with the center verticalhairline constitute first, second, third and fourth alternativeapproximate bullet impact points, respectively, at ranges of 300, 400,500 and 600 yards, respectively.
 13. The reticle in accordance withclaim 12 wherein the approximate bullet impact points in the precedingclaim are operable for a first gun type, and the intersection of thecenter vertical and center horizontal hairlines constitutes a centerpoint which defines an approximate bullet impact point at 100 yards andthe sites of intersection of the first, second, third and fourthrange-markers with the center vertical hairline constitute first,second, third and fourth alternative approximate bullet impact points,respectively, at ranges of 200, 300, 400 and 500 yards, respectively,for a second gun type different from the first gun type.
 14. The reticlein accordance with claim 9 wherein center vertical hairline and thecenter horizontal line each include two radially distal portions eachforming a post having radially directed innermost and outermostextremities.
 15. The reticle in accordance with claim 14 wherein thedistance between the intersection point of the center vertical andcenter horizontal hairlines and each of the innermost extremities of theposts on the center horizontal hairline is about 25 inches.
 16. Atelescopic gunsight comprising: an elongated tubular structure,comprising, a forward objective lens element, a rear lens element, and areticle aligned upon an optical axis with the forward and rear lenselements constituting a line of sight, the reticle comprising, a centervertical hairline and a center horizontal hairline intersecting in anintersection point, a first range-marker disposed below the centerhairline and at a first distance below the center horizontal hairlineand intersecting the center vertical hairline, a second range-markerdisposed below the first range-marker and at a second distance below thecenter horizontal hairline and intersecting the center verticalhairline, a third range-marker disposed below the second range-markerand at a third distance below the center horizontal hairline andintersecting the center vertical hairline, a fourth range-markerdisposed below the third range-marker and at a fourth distance below thehorizontal hairline and intersecting the center vertical hairline, andwherein the various features of the reticle correspond to inches ofsubtention at 100 yards, and the first distance is about 2.0, the seconddistance is about 4.8, the third distance is about 7.5 and the fourthdistance is about 10.5.
 17. The telescopic gunsight in accordance withclaim 16 wherein the first, second, third and fourth range-markers arehorizontal hairlines of sequentially incremental length
 18. Thetelescopic gunsight in accordance with claim 17 wherein the lengths ofthe first, second, third and fourth range marker lines are about 4.12,5.90, 8.32 and 9.72 inches, respectively.
 19. The telescopic gunsight inaccordance with claim 16 wherein the intersection of the center verticaland center horizontal hairlines constitutes a center point which definesan approximate bullet impact point at 100 and 200 yards, and wherein thesites of intersection of the first, second, third and fourthrange-markers with the center vertical hairline constitute first,second, third and fourth alternative approximate bullet impact points,respectively, at ranges of 300, 400, 500 and 600 yards, respectively.20. The reticle in accordance with claim 19 wherein the approximatebullet impact points in the preceding claim are operable when thetelescopic gunsight is used with a first gun type, and the intersectionof the center vertical and center horizontal hairlines constitutes acenter point which defines an approximate bullet impact point at 100yards and the sites of intersection of the first, second, third andfourth range-markers with the center vertical hairline constitute first,second, third and fourth alternative approximate bullet impact points,respectively, at ranges of 200, 300, 400 and 500 yards, respectively,are operable when used with a second gun type different from the firstgun type.
 21. The telescopic gunsight in accordance with claim 16wherein center vertical hairline and the center horizontal line eachinclude two radially distal portions each forming a post having radiallydirected innermost and outermost extremities.
 22. The telescopicgunsight in accordance with claim 21 wherein the distance between theintersection point of the center vertical and center horizontalhairlines and each of the innermost extremities of the posts on thecenter horizontal hairline is about 25 inches.
 23. A gun comprising: ascope having an elongated tubular structure, and further comprising, aforward objective lens element, a rear lens element, and a reticlealigned upon an optical axis with the forward and rear lens elementsconstituting a line of sight, the reticle comprising, a center verticalhairline and a center horizontal hairline intersecting in anintersection point, a first range-marker disposed below the centerhairline and at a first distance below the center horizontal hairlineand intersecting the center vertical hairline, a second range-markerdisposed below the first range-marker and at a second distance below thecenter horizontal hairline and intersecting the center verticalhairline, a third range-marker disposed below the second range-markerand at a third distance below the center horizontal hairline andintersecting the center vertical hairline, a fourth range-markerdisposed below the third range-marker and at a fourth distance below thehorizontal hairline and intersecting the center vertical hairline, andwherein the various features of the reticle correspond to inches ofsubtention at 100 yards, and the first distance is about 2.0, the seconddistance is about 4.8, the third distance is about 7.5 and the fourthdistance is about 10.5.